Question

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Explanation:

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Problem 1:

Step1: Find $\angle DBC$

$\angle DBC = 90^\circ$ (since $\overrightarrow{BD} \perp \overleftrightarrow{ABC}$)

Step2: Find $\angle DBF$

$\angle DBF = \angle DBC - \angle FBC = 90^\circ - 20^\circ = 70^\circ$

Step3: Find $\angle EBD$

$\angle EBD = 90^\circ - \angle DBF = 90^\circ - 70^\circ = 20^\circ$ (since $\overrightarrow{BE} \perp \overrightarrow{BF}$)
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Problem 2:

Step1: Set vertical angles equal

Vertical angles are congruent, so:
$x + 5 = 2x - 5$

Step2: Solve for $x$

$5 + 5 = 2x - x$
$x = 10$

Answer:

1. 20
2. 10